American Institute of Mathematical Sciences

Advanced
April  2017, 13(2): 825-834. doi: 10.3934/jimo.2016048

Robust design of sensor fusion problem in discrete time

Xiao Lan Zhu 1, , Zhi Guo Feng 2,, and  Jian Wen Peng 2,

1. 

LinJiang Middle School, KaiZhou District, Chongqing, China
2. 

College of Mathematical Sciences, Chongqing Normal University, Chongqing, China

* Corresponding author: Hong-Yong Fu

Received  July 2015 Revised  January 2016 Published  August 2016

In this paper, we consider a robust sensor scheduling problem which estimates the state of an uncertain process based on measurements obtained by a given set of noisy sensors, where the measurements of sensors are subject to external interference uncertainties. We formulate this problem into a minimax optimal control problem, which is equivalent to a semi-infinite programming problem with a dynamic system. A discretization method is used to solve this problem, where the computation is very large scale in general. We propose an approximation method to reduce the computational complexity. For illustration, two numerical examples are solved.

Keywords: Robust sensor fusion design, semi-infinite programming.
Mathematics Subject Classification: Primary: 49M37; Secondary: 90C34.
Citation: Xiao Lan Zhu, Zhi Guo Feng, Jian Wen Peng. Robust design of sensor fusion problem in discrete time. Journal of Industrial & Management Optimization, 2017, 13 (2) : 825-834. doi: 10.3934/jimo.2016048
References:
[1]

T. Abburi and S. Narasimhan, Optimal sensor scheduling in batch processes using convex relaxations and tchebycheff systems theory, IEEE Transactions on Automatic Control, 59 (2014), 2978-2983. doi: 10.1109/TAC.2014.2351692. Google Scholar

[2]

Z. L. Deng, Y. Gao, L. Mao, Y. Li and G. Hao, New approach to information fusion steady-state Kalman filtering, Automatica, 41 (2005), 1695-1707. doi: 10.1016/j.automatica.2005.04.020. Google Scholar

[3]

Z. G. Feng, K. L. Teo and Y. Zhao, Branch and bound method for sensor scheduling in discrete time, Journal of Industrial and Management Optimization, 1 (2005), 499-512. doi: 10.3934/jimo.2005.1.499. Google Scholar

[4]

Z. G. Feng, K. L. Teo, N. U. Ahmed, Y. Zhao and W. Y. Yan, Optimal fusion of sensor data for Kalman filtering, Discrete and ContinuousDynamical Systems, 14 (2006), 483-503. Google Scholar

[5]

Z. G. Feng, K. L. Teo, N. U. Ahmed, Y. Zhao and W. Y. Yan, Optimal fusion of sensor data for discrete Kalman filtering, Dynamic Systems and Applications, 16 (2007), 393-406. Google Scholar

[6]

Z. G. Feng, K. L. Teo and V. Rehbock, Hybrid method for a general optimal sensor scheduling problem in discrete time, Automatica, 44 (2008), 1295-1303. doi: 10.1016/j.automatica.2007.09.024. Google Scholar

[7]

F. N. Grigor'ev and N. A. Kuznetsov, Control of the observation process in continuous systems, Problems of Control and Information Theory, 6 (1977), 181-201. Google Scholar

[8]

F. N. Grigor'ev, About the control of information processing in discrete automatic systems, Automation and Remote Control, 43 (1982). Google Scholar

[9]

H. Kushner, On the optimum timing of observations for linear control systems with unknown initial state, IEEE Transactions on Automatic Control, 9 (1964), 144-150. Google Scholar

[10]

H. W. J. Lee, K. L. Teo and L. S. Jennings, Control parametrization enhancing techniques for optimal discrete-valued control problems, Automatica, 35 (1999), 1401-1407. doi: 10.1016/S0005-1098(99)00050-3. Google Scholar

[11]

H. W. J. Lee, K. L. Teo and A. E. B. Lim, Sensor scheduling in continuous time, Automatica, 37 (2001), 2017-2023. doi: 10.1016/S0005-1098(01)00159-5. Google Scholar

[12]

Y. Li, L. W. Krakow, E. K. Chong and K. N. Groom, Approximate stochastic dynamic programming for sensor scheduling to track multiple targets, Digital Signal Processing, 19 (2009), 978-989. doi: 10.1016/j.dsp.2007.05.004. Google Scholar

[13]

J. L. Liu, Y. Sun, J. Yang, W. Y. Liu and W. M. Chen, Optimal sensor scheduling for hybrid estimation, Journal of Central South University, 20 (2013), 2186-2194. doi: 10.1007/s11771-013-1723-4. Google Scholar

[14]

B. M. Miller, Observation control for discrete-continuous stochastic systems, IEEE Transactions on Automatic Control, 45 (2000), 993-998. doi: 10.1109/9.855571. Google Scholar

[15]

V. Malyavej, I. R. Manchester and A. V. Savkin, Precision missile guidance using radar/multiple-video sensor fusion via communication channels with bit-rate constraints, Automatica, 42 (2006), 763-769. doi: 10.1016/j.automatica.2005.12.024. Google Scholar

[16]

A. S. Matveev and A. V. Savki, Optimal state estimation in networked systems with asynchronous communication channels and switched sensors, Journal of optimization theory and applications, 128 (2006), 139-165. doi: 10.1007/s10957-005-7562-1. Google Scholar

[17]

A. V. Savkin, R. J. Evans and E. Skafidas, The problem of optimal robust sensor scheduling, Systems Control Lett., 43 (2001), 149-157. doi: 10.1016/S0167-6911(01)00086-X. Google Scholar

[18]

S. L. Sun, Distributed optimal component fusion weighted by scalars for fixed-lag Kalman smoother, Automatica, 41 (2005), 2153-2159. doi: 10.1016/j.automatica.2005.06.014. Google Scholar

[19]

K. L. Teo, C. Goh and K. Wong, A Unified Computational Approach to Optimal Control Problems, copublished in the United States with John Wiley & Sons, Inc., New York, 1991. Google Scholar

[20]

C. Z. Wu, K. L. Teo and X. Y. Wang, Minimax optimal control of linear system with input-dependent uncertainty, Journal of the Franklin Institute, 351 (2014), 2742-2754. doi: 10.1016/j.jfranklin.2014.01.012. Google Scholar

[21]

C. Z. Wu, K. L. Teo and S. Y. Wu, Min-max optimal control of linear systems with uncertainty and terminal state constraints, Automatica, 49 (2013), 1809-1815. doi: 10.1016/j.automatica.2013.02.052. Google Scholar

[22]

M. Yavuz and D. Jeffcoat, An analysis and solution of the sensor scheduling problem, In Advances in Cooperative Control and Optimization, Springer Berlin Heidelberg, 369 (2007), 167–177. doi: 10.1007/978-3-540-74356-9_10. Google Scholar

show all references

References:
[1]

T. Abburi and S. Narasimhan, Optimal sensor scheduling in batch processes using convex relaxations and tchebycheff systems theory, IEEE Transactions on Automatic Control, 59 (2014), 2978-2983. doi: 10.1109/TAC.2014.2351692. Google Scholar

[2]

Z. L. Deng, Y. Gao, L. Mao, Y. Li and G. Hao, New approach to information fusion steady-state Kalman filtering, Automatica, 41 (2005), 1695-1707. doi: 10.1016/j.automatica.2005.04.020. Google Scholar

[3]

Z. G. Feng, K. L. Teo and Y. Zhao, Branch and bound method for sensor scheduling in discrete time, Journal of Industrial and Management Optimization, 1 (2005), 499-512. doi: 10.3934/jimo.2005.1.499. Google Scholar

[4]

Z. G. Feng, K. L. Teo, N. U. Ahmed, Y. Zhao and W. Y. Yan, Optimal fusion of sensor data for Kalman filtering, Discrete and ContinuousDynamical Systems, 14 (2006), 483-503. Google Scholar

[5]

Z. G. Feng, K. L. Teo, N. U. Ahmed, Y. Zhao and W. Y. Yan, Optimal fusion of sensor data for discrete Kalman filtering, Dynamic Systems and Applications, 16 (2007), 393-406. Google Scholar

[6]

Z. G. Feng, K. L. Teo and V. Rehbock, Hybrid method for a general optimal sensor scheduling problem in discrete time, Automatica, 44 (2008), 1295-1303. doi: 10.1016/j.automatica.2007.09.024. Google Scholar

[7]

F. N. Grigor'ev and N. A. Kuznetsov, Control of the observation process in continuous systems, Problems of Control and Information Theory, 6 (1977), 181-201. Google Scholar

[8]

F. N. Grigor'ev, About the control of information processing in discrete automatic systems, Automation and Remote Control, 43 (1982). Google Scholar

[9]

H. Kushner, On the optimum timing of observations for linear control systems with unknown initial state, IEEE Transactions on Automatic Control, 9 (1964), 144-150. Google Scholar

[10]

H. W. J. Lee, K. L. Teo and L. S. Jennings, Control parametrization enhancing techniques for optimal discrete-valued control problems, Automatica, 35 (1999), 1401-1407. doi: 10.1016/S0005-1098(99)00050-3. Google Scholar

[11]

H. W. J. Lee, K. L. Teo and A. E. B. Lim, Sensor scheduling in continuous time, Automatica, 37 (2001), 2017-2023. doi: 10.1016/S0005-1098(01)00159-5. Google Scholar

[12]

Y. Li, L. W. Krakow, E. K. Chong and K. N. Groom, Approximate stochastic dynamic programming for sensor scheduling to track multiple targets, Digital Signal Processing, 19 (2009), 978-989. doi: 10.1016/j.dsp.2007.05.004. Google Scholar

[13]

J. L. Liu, Y. Sun, J. Yang, W. Y. Liu and W. M. Chen, Optimal sensor scheduling for hybrid estimation, Journal of Central South University, 20 (2013), 2186-2194. doi: 10.1007/s11771-013-1723-4. Google Scholar

[14]

B. M. Miller, Observation control for discrete-continuous stochastic systems, IEEE Transactions on Automatic Control, 45 (2000), 993-998. doi: 10.1109/9.855571. Google Scholar

[15]

V. Malyavej, I. R. Manchester and A. V. Savkin, Precision missile guidance using radar/multiple-video sensor fusion via communication channels with bit-rate constraints, Automatica, 42 (2006), 763-769. doi: 10.1016/j.automatica.2005.12.024. Google Scholar

[16]

A. S. Matveev and A. V. Savki, Optimal state estimation in networked systems with asynchronous communication channels and switched sensors, Journal of optimization theory and applications, 128 (2006), 139-165. doi: 10.1007/s10957-005-7562-1. Google Scholar

[17]

A. V. Savkin, R. J. Evans and E. Skafidas, The problem of optimal robust sensor scheduling, Systems Control Lett., 43 (2001), 149-157. doi: 10.1016/S0167-6911(01)00086-X. Google Scholar

[18]

S. L. Sun, Distributed optimal component fusion weighted by scalars for fixed-lag Kalman smoother, Automatica, 41 (2005), 2153-2159. doi: 10.1016/j.automatica.2005.06.014. Google Scholar

[19]

K. L. Teo, C. Goh and K. Wong, A Unified Computational Approach to Optimal Control Problems, copublished in the United States with John Wiley & Sons, Inc., New York, 1991. Google Scholar

[20]

C. Z. Wu, K. L. Teo and X. Y. Wang, Minimax optimal control of linear system with input-dependent uncertainty, Journal of the Franklin Institute, 351 (2014), 2742-2754. doi: 10.1016/j.jfranklin.2014.01.012. Google Scholar

[21]

C. Z. Wu, K. L. Teo and S. Y. Wu, Min-max optimal control of linear systems with uncertainty and terminal state constraints, Automatica, 49 (2013), 1809-1815. doi: 10.1016/j.automatica.2013.02.052. Google Scholar

[22]

M. Yavuz and D. Jeffcoat, An analysis and solution of the sensor scheduling problem, In Advances in Cooperative Control and Optimization, Springer Berlin Heidelberg, 369 (2007), 167–177. doi: 10.1007/978-3-540-74356-9_10. Google Scholar

Figure 1.  Optimal solutions in the first example
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 2.  he cost function values in the first example
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 3.  Optimal solutions of the second example
Figure Options

Download full-size image

Download as PowerPoint slide

[1]

Yanqun Liu, Ming-Fang Ding. A ladder method for linear semi-infinite programming. Journal of Industrial & Management Optimization, 2014, 10 (2) : 397-412. doi: 10.3934/jimo.2014.10.397
[2]

Cheng Ma, Xun Li, Ka-Fai Cedric Yiu, Yongjian Yang, Liansheng Zhang. On an exact penalty function method for semi-infinite programming problems. Journal of Industrial & Management Optimization, 2012, 8 (3) : 705-726. doi: 10.3934/jimo.2012.8.705
[3]

Zhi Guo Feng, Kok Lay Teo, Volker Rehbock. A smoothing approach for semi-infinite programming with projected Newton-type algorithm. Journal of Industrial & Management Optimization, 2009, 5 (1) : 141-151. doi: 10.3934/jimo.2009.5.141
[4]

Jinchuan Zhou, Changyu Wang, Naihua Xiu, Soonyi Wu. First-order optimality conditions for convex semi-infinite min-max programming with noncompact sets. Journal of Industrial & Management Optimization, 2009, 5 (4) : 851-866. doi: 10.3934/jimo.2009.5.851
[5]

Jinchuan Zhou, Naihua Xiu, Jein-Shan Chen. Solution properties and error bounds for semi-infinite complementarity problems. Journal of Industrial & Management Optimization, 2013, 9 (1) : 99-115. doi: 10.3934/jimo.2013.9.99
[6]

Burcu Özçam, Hao Cheng. A discretization based smoothing method for solving semi-infinite variational inequalities. Journal of Industrial & Management Optimization, 2005, 1 (2) : 219-233. doi: 10.3934/jimo.2005.1.219
[7]

Z. G. Feng, Kok Lay Teo, N. U. Ahmed, Yulin Zhao, W. Y. Yan. Optimal fusion of sensor data for Kalman filtering. Discrete & Continuous Dynamical Systems - A, 2006, 14 (3) : 483-503. doi: 10.3934/dcds.2006.14.483
[8]

Rafael del Rio, Mikhail Kudryavtsev, Luis O. Silva. Inverse problems for Jacobi operators III: Mass-spring perturbations of semi-infinite systems. Inverse Problems & Imaging, 2012, 6 (4) : 599-621. doi: 10.3934/ipi.2012.6.599
[9]

Igor Chueshov. Remark on an elastic plate interacting with a gas in a semi-infinite tube: Periodic solutions. Evolution Equations & Control Theory, 2016, 5 (4) : 561-566. doi: 10.3934/eect.2016019
[10]

Roman Chapko, B. Tomas Johansson. An alternating boundary integral based method for a Cauchy problem for the Laplace equation in semi-infinite regions. Inverse Problems & Imaging, 2008, 2 (3) : 317-333. doi: 10.3934/ipi.2008.2.317
[11]

Meixia Li, Changyu Wang, Biao Qu. Non-convex semi-infinite min-max optimization with noncompact sets. Journal of Industrial & Management Optimization, 2017, 13 (4) : 1859-1881. doi: 10.3934/jimo.2017022
[12]

Xiaodong Fan, Tian Qin. Stability analysis for generalized semi-infinite optimization problems under functional perturbations. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-13. doi: 10.3934/jimo.2018201
[13]

Azhar Ali Zafar, Khurram Shabbir, Asim Naseem, Muhammad Waqas Ashraf. MHD natural convection boundary-layer flow over a semi-infinite heated plate with arbitrary inclination. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 1007-1015. doi: 10.3934/dcdss.2020059
[14]

Atul Kumar, R. R. Yadav. Analytical approach of one-dimensional solute transport through inhomogeneous semi-infinite porous domain for unsteady flow: Dispersion being proportional to square of velocity. Conference Publications, 2013, 2013 (special) : 457-466. doi: 10.3934/proc.2013.2013.457
[15]

Magdi S. Mahmoud, Omar Al-Buraiki. Robust control design of autonomous bicycle kinematics. Numerical Algebra, Control & Optimization, 2014, 4 (3) : 181-191. doi: 10.3934/naco.2014.4.181
[16]

Changzhi Wu, Chaojie Li, Qiang Long. A DC programming approach for sensor network localization with uncertainties in anchor positions. Journal of Industrial & Management Optimization, 2014, 10 (3) : 817-826. doi: 10.3934/jimo.2014.10.817
[17]

Ruotian Gao, Wenxun Xing. Robust sensitivity analysis for linear programming with ellipsoidal perturbation. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-16. doi: 10.3934/jimo.2019041
[18]

Hui Zhang, Jian-Feng Cai, Lizhi Cheng, Jubo Zhu. Strongly convex programming for exact matrix completion and robust principal component analysis. Inverse Problems & Imaging, 2012, 6 (2) : 357-372. doi: 10.3934/ipi.2012.6.357
[19]

Cecilia Cavaterra, M. Grasselli. Robust exponential attractors for population dynamics models with infinite time delay. Discrete & Continuous Dynamical Systems - B, 2006, 6 (5) : 1051-1076. doi: 10.3934/dcdsb.2006.6.1051
[20]

Vadim Azhmyakov, Alex Poznyak, Omar Gonzalez. On the robust control design for a class of nonlinearly affine control systems: The attractive ellipsoid approach. Journal of Industrial & Management Optimization, 2013, 9 (3) : 579-593. doi: 10.3934/jimo.2013.9.579

2018 Impact Factor: 1.025

Tools

Metrics

  • PDF downloads (21)
  • HTML views (297)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences